A critique of scaling behaviour in non-linear structure formation scenarios

Abstract

Moments of the BBGKY equations for spatial correlation functions of cosmological density perturbations are used to obtain a differential equation for the evolution of the dimensionless function, $h=-(v/\dot{a}x)$, where $v$ is the mean relative pair velocity. The BBGKY equations are closed using a hierarchical scaling ansatz for the 3-point correlation function. Scale-invariant solutions derived earlier by Davis and Peebles are then used in the non-linear regime, along with the generalised stable clustering hypothesis ($h\to$ const.), to obtain an expression for the asymptotic value of $h$, in terms of the power law index of clustering, $\gamma$,and the tangential and radial velocity dispersions. The Davis-Peebles solution is found to require that tangential dispersions are larger than radial ones, in the non-linear regime; this can be understood on physical grounds. Finally, stability analysis of the solution demonstrates that the allowed asymptotic values of $h$, consistent with the stable clustering hypothesis, lie in the range $0\le h\le 1/2$. Thus, if the Davis-Peebles scale-invariant solution (and the hierarchical model for the 3-pt function) is correct, the standard stable clustering picture ($h\to 1$ as $\bar{\xi }\to \infty$) is not allowed in the non-linear regime of structure formation.

14 pages, no figures. Scheduled to appear in ApJ, Mar 1 issue. Final version, contains added discussion to match the accepted version

References in corpus (4)

• Pattern in Nonlinear Gravatational Clustering: A Numerical Investigation
• Nonlinear Gravitational Clustering: dreams of a paradigm
• Scale-Invariant Correlation Functions of Cosmological Density Fluctuations in the Strong Clustering Regime
• Nonlinear Gravitational Clustering in Expanding Universe

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